Which of the following equations has the solution set x={−9/5 , 3}

Question

?(1 point)
Responses

−3x(5x+9)=0

negative 3 x left parenthesis 5 x plus 9 right parenthesis equals 0
(x−3)(5x+9)=0
left parenthesis x minus 3 right parenthesis left parenthesis 5 x plus 9 right parenthesis equals 0
(x+3)(9x−5)=0
left parenthesis x plus 3 right parenthesis left parenthesis 9 x minus 5 right parenthesis equals 0
(x−3)(9x+5)=0

Answer 1

To find out which equation has the solution set \( x = {-\frac{9}{5}, 3} \), we can analyze each of the given equations by identifying their roots.

1. Equation: \(-3x(5x+9)=0\)

   • Setting each factor to zero:

     • \(-3x = 0\) ⇒ \(x = 0\)
     • \(5x + 9 = 0\) ⇒ \(5x = -9\) ⇒ \(x = -\frac{9}{5}\)

   • Solution set: \( x = {0, -\frac{9}{5}} \)

2. Equation: \((x−3)(5x+9)=0\)

   • Setting each factor to zero:

     • \(x - 3 = 0\) ⇒ \(x = 3\)
     • \(5x + 9 = 0\) ⇒ \(x = -\frac{9}{5}\)

   • Solution set: \( x = {3, -\frac{9}{5}} \)

3. Equation: \((x+3)(9x−5)=0\)

   • Setting each factor to zero:

     • \(x + 3 = 0\) ⇒ \(x = -3\)
     • \(9x - 5 = 0\) ⇒ \(9x = 5\) ⇒ \(x = \frac{5}{9}\)

   • Solution set: \( x = {-3, \frac{5}{9}} \)

4. Equation: \((x−3)(9x+5)=0\)

   • Setting each factor to zero:

     • \(x - 3 = 0\) ⇒ \(x = 3\)
     • \(9x + 5 = 0\) ⇒ \(9x = -5\) ⇒ \(x = -\frac{5}{9}\)

   • Solution set: \( x = {3, -\frac{5}{9}} \)

From our analysis, the equation that has the solution set \( x = {-\frac{9}{5}, 3} \) is:

\((x−3)(5x+9)=0\).

Thus, the correct response is:

\((x−3)(5x+9)=0\).